Dear Wilhelmus,
I am also glad to see you at this Contest!
Thanks for reading my essay and comment.
As for the paradigm problems in Computational mathematics, I cited excerpts from the article Mathematics XXI - a radical paradigm shift. Model, not Algorithm by mathematician A.Narin'yani . The author concludes:
«Computational mathematics in the coming years will radically change the paradigm and move into a new quality.
The main content of Computational mathematics will be the qualitative promotion of several basic closely related components:
-The development of the theory of knowledge representation and the corresponding apparatus for describing Models,...
-Development of modeling technologies, optimization of the process of "functioning of the Model" itself,...
-Development, i.e. expansion and efficiency of the universal procedure for compressing the modeling space to highlight the solution body..."
As for dialectics and the history of its development, I set the task of its rehabilitation as an effective method of solving the key problems of fundamental science, primarily in understanding matter and space, their ontological structure.
I believe that «Model» and «Algorithm» should not be in the dialectical "struggle" for primacy, but should work in a reliable dialectical unity...
As the 60s student song says:
"I know that dialectics will develop everything,
But when I will be gone.
Mankind will have everything
And I would have to get the fire... " (A. Genkin)
I'm already starting to read your essay.
Respectfully,
Vladimir